As the above answer says, but this link explains a bit futher, also, not mentioned on this link, is the fact that Greys also take young birds and eggs.
the reasons for the decline of the red are more complex than being driven out by grays which is a bit of a myth. In fact the two species do not fight. It seems to be competition for food and simply the fact that the greys are more adaptable and will eat a wider range of food. Greys will adapt to live in parks, hedges etc which reds will not- they need woodland. A given area will support a much greater density of greys than reds.
Oh- and reds have been recorded taking birds eggs as well!
Actually its because the schools are much better, and there are no council houses with the usual problems that brings. Also no late night take aways, and pubs that turn out causing lots of noise and yobs puking all over the hedges.